All Questions

I am trying to simplify the following limit of integral where $\mu$ is given: $$p(y) = \lim_{\sigma \to 0} \int_{\mathbb R} |x| \cdot \frac{1}{\sqrt{2\pi\sigma^2} } e^{-\frac{1}{2\sigma^2} (xy - \mu)^...

Let $\mathcal{P}_p(X)$ denote the Wasserstein space over a compact metric space $X$, and $1\leq p<\infty$. Fix a non-empty closed subset $C\subseteq X$. Then is the map: $$ \mathbb{P} \mapsto \...

Given a Riemannian manifold $(\mathcal{M}, \{g_x\}_{x \in \mathcal{M}})$ and a fixed point $x \in \mathcal{M}$, does the following procedure yield uniform samples from $\{y \in \mathcal{M} : d_\...

Motivation: I want to compute $$E[g(X)] := \int_{\Omega} g(X(\omega)) d\mathbb{P}(\omega) \tag{*}$$ without needing change of variable formula. I want to prove the change of variable formula (you ...

This builds off on an old question about mixture measures: Generalized notions of mixture Suppose $\mathcal{M}$ is a family of probability measures, and $Q$ is a probability measure over $\mathcal{M}$...

I'm reading the probabilistic book write by çinlar, but I don't understand the Kernel theory, in details: $ (E,\mathcal{E}),(F,\mathcal{F})$ are two measurable space $$K:E \times \mathcal{F} \...